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'''Note on notation.''' When there is only one sign relation <math>L_J = L(J)</math> associated with a given interpreter <math>J</math>, it is convenient to use the following forms of abbreviation:
'''Note on notation.''' When there is only one sign relation <math>L_J = L(J)</math> associated with a given interpreter <math>J</math>, it is convenient to use the following forms of abbreviation:
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:{| cellpadding=4
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{| align="center" cellspacing="6" width="90%"
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| ''J''<sub>''OS''</sub>
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|
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| = || ''Den''(''L''<sub>''J'' </sub>)
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<math>\begin{array}{lclclclcl}
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| = || ''Proj''<sub>''OS'' </sub>''L''<sub>''J''</sub>
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J_{OS}
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| = || (''L''<sub>''J'' </sub>)<sub>''OS''</sub>
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& = & \operatorname{Den}(L_J)
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| = || ''L''(''J'')<sub>''OS''</sub>
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& = & \operatorname{proj}_{OS} L_J
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|-
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& = & (L_J)_{OS}
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| ''J''<sub>''SI''</sub>
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& = & L(J)_{OS}
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| = || ''Con''(''L''<sub>''J'' </sub>)
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\\[6pt]
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| = || ''Proj''<sub>''SI'' </sub>''L''<sub>''J''</sub>
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J_{SI}
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| = || (''L''<sub>''J'' </sub>)<sub>''SI''</sub>
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& = & \operatorname{Con}(L_J)
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| = || ''L''(''J'')<sub>''SI''</sub>
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& = & \operatorname{proj}_{SI} L_J
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|-
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& = & (L_J)_{SI}
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| ''J''<sub>''OI''</sub>
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& = & L(J)_{SI}
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| = || ''Int''(''L''<sub>''J'' </sub>)
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\\[6pt]
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| = || ''Proj''<sub>''OI'' </sub>''L''<sub>''J''</sub>
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J_{OI}
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| = || (''L''<sub>''J'' </sub>)<sub>''OI''</sub>
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& = & \operatorname{Int}(L_J)
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| = || ''L''(''J'')<sub>''OI''</sub>
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& = & \operatorname{proj}_{OI} L_J
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& = & (L_J)_{OI}
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& = & L(J)_{OI}
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\end{array}</math>
|}
|}